As of 2010, Crossley is Emeritus Professor of Logic[1] at Monash University, Australia where he has been connected since 1968. Crossley studied at Oxford University where he received his DPhil and MA (Mathematics) in 1963. His early career was spent at Oxford where he was the first university lecturer in mathematical logic and was a Fellow of All Souls College, Oxford. He is still a Quondam Fellow there.[2] He was offered a Readership position and following a lecturing visit to Monash University in 1968, he was elected to a Chair in Pure Mathematics. He accepted this position and as of 2010, Crossley continues to be active at Monash University where he serves through its Faculty of Information Technology.

Crossley has written books in logic, mathematics and computer science. His is known as the lead author of the book What is Mathematical Logic.[3][4] Co-written by some of his students, the book popularized the subject to the interested layman. Many of Crossley's doctoral students[5] have gone on to be professors themselves and have written books in the field of mathematics or computing, including Peter Aczel, Wilfrid Hodges, John Lane Bell and Rod Downey.

Crossley is also an avid photographer. In 1974 he first exhibited his photographs in Melbourne and again 2005 he exhibited Composition and Context,[6] a collection of photographs shot by Crossley around the world that illustrates the title and theme of the exhibition. A number of these photographs since have appeared in publications in Australia, Britain and the Philippines.